Best Known (80−29, 80, s)-Nets in Base 64
(80−29, 80, 690)-Net over F64 — Constructive and digital
Digital (51, 80, 690)-net over F64, using
- 3 times m-reduction [i] based on digital (51, 83, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (28, 60, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- digital (7, 23, 177)-net over F64, using
- (u, u+v)-construction [i] based on
(80−29, 80, 4681)-Net in Base 64 — Constructive
(51, 80, 4681)-net in base 64, using
- 644 times duplication [i] based on (47, 76, 4681)-net in base 64, using
- base change [i] based on digital (28, 57, 4681)-net over F256, using
- net defined by OOA [i] based on linear OOA(25657, 4681, F256, 29, 29) (dual of [(4681, 29), 135692, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25657, 65535, F256, 29) (dual of [65535, 65478, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25657, 65535, F256, 29) (dual of [65535, 65478, 30]-code), using
- net defined by OOA [i] based on linear OOA(25657, 4681, F256, 29, 29) (dual of [(4681, 29), 135692, 30]-NRT-code), using
- base change [i] based on digital (28, 57, 4681)-net over F256, using
(80−29, 80, 25966)-Net over F64 — Digital
Digital (51, 80, 25966)-net over F64, using
(80−29, 80, large)-Net in Base 64 — Upper bound on s
There is no (51, 80, large)-net in base 64, because
- 27 times m-reduction [i] would yield (51, 53, large)-net in base 64, but